Conventional methods for generating a tone signal include direct analog generation of a low frequency tone signal using a digital-analog converter with a sampling rate of at least twice the tone frequency of the tone signal and multiple bits of resolution. It is possible to modulate the generated tone signal onto an optical or electrical carrier. The modulation of the tone signal requires a linear modulation unit to avoid the generation of harmonics. Generating an analog tone signal from a digital signal can be performed by modulating a mark density of a binary signal and by filtering this binary signal. A sigma-delta conversion can be used to generate a binary bit sequence with a minimum of spurious frequencies within a range of interest. However, the rate of the binary bit sequence or binary bit stream in this conventional approach must be at least a multiple of 16 to 20 of the highest tone frequency, e.g. performing an oversampling with at least a factor of 8.
Table 1 illustrates a mark density modulated bit sequence comprising four periods each having 8 bits which can be generated by sigma-delta conversion.
TABLE 1−1111−11−1−11111−1−1−1−11−111−1−1−11−1111−1−1−11
The bit sequence illustrated in Table 1 yields a signal spectrum as illustrated in FIG. 1A with a basic frequency fb of 25 kHz. The basic frequency corresponds to the repletion rate of the bit sequence and equals to the bit rate (800 kbit/s in the example) divided by the length of the bit sequence (32 bits in the example). The spectrum shows a tone signal at a tone frequency of 100 kHz. The sigma-delta conversion shown in the example is based on an oversampling with an oversampling rate OSR of only 4 in order to reduce the bit sequence lengths. This results in relatively large spurious frequency components in the frequency range of interest. A larger oversampling with a higher oversampling rate OSR reduces these frequency components as also illustrated in FIG. 1B where an oversampling rate OSR of 11 was applied for a maximum tone frequency being 80 times the repetition rate of the bit sequence. In the spectrum of FIG. 1A, the oversampling rate OSR is four (OSR=4) for the bit sequence illustrated in Table 1 having 4 periods T each comprising eight bits. In contrast, the bit sequence used for the spectrum illustrated in FIG. 1B uses a bit sequence comprising 80 periods each comprising 22 bits for a maximum tone frequency fmax=80 resulting in a bit sequence length of 2×11×80=1760 bits. By comparing FIG. 1A and FIG. 1B, it can be seen that the noise-free range is expanded in FIG. 1B.
By increasing the sampling rate, i.e. by repeating each bit the resulting spectrum is not changed. Table 2 illustrates a bit sequence which is generated by resampling the bit sequence of Table 1 with twice the bit rate.
TABLE 2−1−1111111−1−111−1−1−1−111111111−1−1−1−1−1−1−1−111−1−11111−1−1−1−1−1−111−1−1111111−1−1−1−1−1−111
FIG. 2A illustrates a signal spectrum of a sigma-delta generated bit stream with a tone signal at f/fb=4 with a higher sampling rate whereas FIG. 2B illustrates a signal spectrum of a resampled signal similar to FIG. 1B.
A multiplication by an alternating sequence +1/−1, e.g. by a Manchester encoding, shifts the signal spectrum to the frequency range around the fundamental frequency of the alternating sequence, in the illustrated example fb=32.
Table 3 illustrates a bit sequence which is generated by multiplying the bit sequence of Table 2 with a +1/−1 alternating binary sequence.
TABLE 3−111−11−11−1−111−1−11−111−11−11−11−1−11−11−11−111−1−111−11−1−11−11−111−1−111−11−11−1−11−11−111−1
FIG. 3A illustrates a spectrum of the sigma-delta generated bit stream multiplied by the alternating sequence as indicated in Table 3 resulting in a tone signal around fb=32. FIG. 3B illustrates the signal spectrum of a signal shown in FIG. 2B multiplied by the alternating +1/−1 periodic sequence.
The sampling rate can be further increased, for instance doubled. Table 4 illustrates a bit sequence generated by resampling the bit sequence of Table 3 with twice the bit rate.
TABLE 4−1−11111−1−111−1−111−1−1−1−1111−1−111−1−111−1−111−1−1−1−1111−1−1−1−11111−1−111−1−1−1−11−1−11111−1−111−1−111−1−1−1−11111−1−1−1−111−1−1111−1−111−1−111−1−1111−1−111−1−11111−1−11−1−111−1−11111−1−1
The resulting spectrum (now also illustrating higher frequencies) shows lines separated by +/−4 from the normalized frequency f/fb of 32.
FIG. 4A illustrates a signal spectrum of a sigma-delta generated bit stream multiplied by a −1/1 alternating periodic bit sequence with a higher sampling rate or bit rate as illustrated in Table 4 resulting in tone signal components at frequencies f/fb=32±4=28 (700 kHz) and 36 (900 kHz).
FIG. 4B illustrates a signal spectrum of the resampled signal of FIG. 3B showing tone signal components at normalized frequencies f/fb=1760±43=1717 and 1803.
In the conventional methods for generating a tone signal, the ratio of the bit rate to the tone frequency of the generated tone signal is high. Accordingly, the technical complexity of the tone signal generator is high and requires a high clock rate. Consequently, the consumed electrical power is increased because of the high clock rate.
Accordingly there is a need to provide a method and apparatus which allows to generate a tone signal with a low clock rate.